Stochastic Model Reconstruction From Incomplete Noisy Measurements

A technique of reconstruction of both unknown state and unknown vector-field of stochastic nonlinear dynamical system is introduced. It is based on the application of the path-integral theory to the full Bayesian inference and extended Kalman filter theory. We illustrate the application of this technique to the reconstruction of the model of FitzHugh-Nagumo oscillator from the corrupted by noise measurements. A number of important unsolved problems is identified.